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[u/mdw/catacomb] / mp-arith.c
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d3409d5e 1/* -*-c-*-
2 *
a9c8f3d6 3 * $Id: mp-arith.c,v 1.17 2003/10/12 15:03:35 mdw Exp $
d3409d5e 4 *
5 * Basic arithmetic on multiprecision integers
6 *
7 * (c) 1999 Straylight/Edgeware
8 */
9
10/*----- Licensing notice --------------------------------------------------*
11 *
12 * This file is part of Catacomb.
13 *
14 * Catacomb is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU Library General Public License as
16 * published by the Free Software Foundation; either version 2 of the
17 * License, or (at your option) any later version.
18 *
19 * Catacomb is distributed in the hope that it will be useful,
20 * but WITHOUT ANY WARRANTY; without even the implied warranty of
21 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22 * GNU Library General Public License for more details.
23 *
24 * You should have received a copy of the GNU Library General Public
25 * License along with Catacomb; if not, write to the Free
26 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
27 * MA 02111-1307, USA.
28 */
29
30/*----- Revision history --------------------------------------------------*
31 *
32 * $Log: mp-arith.c,v $
a9c8f3d6 33 * Revision 1.17 2003/10/12 15:03:35 mdw
34 * Merge fix from other branch.
35 *
36 * Revision 1.16.2.1 2003/06/10 13:21:10 mdw
37 * Fix bug dividing small things by large ones.
38 *
81578196 39 * Revision 1.16 2003/05/16 09:09:24 mdw
40 * Fix @mp_lsl2c@. Turns out to be surprisingly tricky.
41 *
75263f25 42 * Revision 1.15 2002/10/19 17:56:50 mdw
43 * Fix bit operations. Test them (a bit) better.
44 *
397041a9 45 * Revision 1.14 2002/10/15 19:18:31 mdw
46 * New operation to negate numbers.
47 *
09d00c6b 48 * Revision 1.13 2002/10/15 00:19:40 mdw
49 * Bit setting and clearing functions.
50 *
dd22938e 51 * Revision 1.12 2002/10/09 00:36:03 mdw
52 * Fix bounds on workspace for Karatsuba operations.
53 *
f09e814a 54 * Revision 1.11 2002/10/06 22:52:50 mdw
55 * Pile of changes for supporting two's complement properly.
56 *
0f32e0f8 57 * Revision 1.10 2001/04/03 19:36:05 mdw
58 * Add some simple bitwise operations so that Perl can use them.
59 *
52cdaca9 60 * Revision 1.9 2000/10/08 15:48:35 mdw
61 * Rename Karatsuba constants now that we have @gfx_kmul@ too.
62 *
4b536f42 63 * Revision 1.8 2000/10/08 12:02:21 mdw
64 * Use @MP_EQ@ instead of @MP_CMP@.
65 *
f1713c63 66 * Revision 1.7 2000/06/22 19:02:53 mdw
67 * New function @mp_odd@ to extract powers of two from an integer. This is
68 * common code from the Rabin-Miller test, RSA key recovery and modular
69 * square-root extraction.
70 *
d34decd2 71 * Revision 1.6 2000/06/17 11:45:09 mdw
72 * Major memory management overhaul. Added arena support. Use the secure
73 * arena for secret integers. Replace and improve the MP management macros
74 * (e.g., replace MP_MODIFY by MP_DEST).
75 *
bba03f55 76 * Revision 1.5 1999/12/22 15:54:41 mdw
77 * Adjust Karatsuba parameters. Calculate destination size better.
78 *
8017495b 79 * Revision 1.4 1999/12/13 15:35:16 mdw
80 * Slightly different rules on memory allocation.
81 *
5bf74dea 82 * Revision 1.3 1999/12/11 10:57:43 mdw
83 * Karatsuba squaring algorithm.
84 *
ef5f4810 85 * Revision 1.2 1999/12/10 23:18:39 mdw
86 * Change interface for suggested destinations.
87 *
d3409d5e 88 * Revision 1.1 1999/11/17 18:02:16 mdw
89 * New multiprecision integer arithmetic suite.
90 *
91 */
92
93/*----- Header files ------------------------------------------------------*/
94
95#include "mp.h"
96
ef5f4810 97/*----- Macros ------------------------------------------------------------*/
98
99#define MAX(x, y) ((x) >= (y) ? (x) : (y))
100
d3409d5e 101/*----- Main code ---------------------------------------------------------*/
102
81578196 103/* --- @mp_lsl@, @mp_lslc@, @mp_lsr@ --- *
d3409d5e 104 *
f09e814a 105 * Arguments: @mp *d@ = destination
106 * @mp *a@ = source
107 * @size_t n@ = number of bits to move
d3409d5e 108 *
f09e814a 109 * Returns: Result, @a@ shifted left or right by @n@.
81578196 110 *
111 * Use: Bitwise shift operators. @mp_lslc@ fills the bits introduced
112 * on the right with ones instead of zeroes: it's used
113 * internally by @mp_lsl2c@, though it may be useful on its
114 * own.
d3409d5e 115 */
116
f09e814a 117mp *mp_lsl(mp *d, mp *a, size_t n)
d3409d5e 118{
f09e814a 119 MP_DEST(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS, a->f);
120 mpx_lsl(d->v, d->vl, a->v, a->vl, n);
121 d->f = a->f & (MP_NEG | MP_BURN);
122 MP_SHRINK(d);
123 return (d);
124}
d3409d5e 125
81578196 126mp *mp_lslc(mp *d, mp *a, size_t n)
127{
128 MP_DEST(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS, a->f);
129 mpx_lslc(d->v, d->vl, a->v, a->vl, n);
130 d->f = a->f & (MP_NEG | MP_BURN);
131 MP_SHRINK(d);
132 return (d);
133}
134
f09e814a 135mp *mp_lsr(mp *d, mp *a, size_t n)
136{
d34decd2 137 MP_DEST(d, MP_LEN(a), a->f);
f09e814a 138 mpx_lsr(d->v, d->vl, a->v, a->vl, n);
139 d->f = a->f & (MP_NEG | MP_BURN);
d3409d5e 140 MP_SHRINK(d);
141 return (d);
142}
143
f09e814a 144/* --- @mp_lsl2c@, @mp_lsr2c@ --- *
d3409d5e 145 *
146 * Arguments: @mp *d@ = destination
147 * @mp *a@ = source
f09e814a 148 * @size_t n@ = number of bits to move
d3409d5e 149 *
f09e814a 150 * Returns: Result, @a@ shifted left or right by @n@. Handles the
151 * pretence of sign-extension for negative numbers.
d3409d5e 152 */
153
f09e814a 154mp *mp_lsl2c(mp *d, mp *a, size_t n)
d3409d5e 155{
f09e814a 156 if (!(a->f & MP_NEG))
157 return (mp_lsl(d, a, n));
158 d = mp_not2c(d, a);
81578196 159 d = mp_lslc(d, d, n);
f09e814a 160 d = mp_not2c(d, d);
161 return (d);
162}
d3409d5e 163
f09e814a 164mp *mp_lsr2c(mp *d, mp *a, size_t n)
165{
166 if (!(a->f & MP_NEG))
167 return (mp_lsr(d, a, n));
168 d = mp_not2c(d, a);
169 d = mp_lsr(d, d, n);
170 d = mp_not2c(d, d);
171 return (d);
d3409d5e 172}
173
f09e814a 174/* --- @mp_testbit@ --- *
d3409d5e 175 *
f09e814a 176 * Arguments: @mp *x@ = a large integer
09d00c6b 177 * @unsigned long n@ = which bit to test
d3409d5e 178 *
f09e814a 179 * Returns: Nonzero if the bit is set, zero if not.
d3409d5e 180 */
181
09d00c6b 182int mp_testbit(mp *x, unsigned long n)
d3409d5e 183{
f09e814a 184 if (n > MPW_BITS * MP_LEN(x))
185 return (0);
09d00c6b 186 return ((x->v[n/MPW_BITS] >> n%MPW_BITS) & 1u);
d3409d5e 187}
188
f09e814a 189/* --- @mp_testbit2c@ --- *
d3409d5e 190 *
f09e814a 191 * Arguments: @mp *x@ = a large integer
09d00c6b 192 * @unsigned long n@ = which bit to test
d3409d5e 193 *
f09e814a 194 * Returns: Nonzero if the bit is set, zero if not. Fakes up two's
195 * complement representation.
d3409d5e 196 */
197
09d00c6b 198int mp_testbit2c(mp *x, unsigned long n)
d3409d5e 199{
f09e814a 200 int r;
09d00c6b 201 if (!(x->f & MP_NEG))
f09e814a 202 return (mp_testbit(x, n));
203 x = mp_not2c(MP_NEW, x);
204 r = !mp_testbit(x, n);
205 MP_DROP(x);
206 return (r);
d3409d5e 207}
208
09d00c6b 209/* --- @mp_setbit@, @mp_clearbit@ --- *
210 *
211 * Arguments: @mp *d@ = a destination
212 * @mp *x@ = a large integer
213 * @unsigned long n@ = which bit to modify
214 *
215 * Returns: The argument @x@, with the appropriate bit set or cleared.
216 */
217
218mp *mp_setbit(mp *d, mp *x, unsigned long n)
219{
220 size_t rq;
221
222 rq = n + MPW_BITS; rq -= rq % MPW_BITS;
223 if (d != x) {
224 if (d) MP_DROP(d);
225 d = MP_COPY(x);
226 }
227 MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN));
228 d->v[n/MPW_BITS] |= 1 << n%MPW_BITS;
229 return (d);
230}
231
232mp *mp_clearbit(mp *d, mp *x, unsigned long n)
233{
234 size_t rq;
235
236 rq = n + MPW_BITS; rq -= rq % MPW_BITS;
237 if (d != x) {
238 if (d) MP_DROP(d);
239 d = MP_COPY(x);
240 }
241 MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN));
242 d->v[n/MPW_BITS] &= ~(1 << n%MPW_BITS);
243 return (d);
244}
245
246/* --- @mp_setbit2c@, @mp_clearbit2c@ --- *
247 *
248 * Arguments: @mp *d@ = a destination
249 * @mp *x@ = a large integer
250 * @unsigned long n@ = which bit to modify
251 *
252 * Returns: The argument @x@, with the appropriate bit set or cleared.
253 * Fakes up two's complement representation.
254 */
255
256mp *mp_setbit2c(mp *d, mp *x, unsigned long n)
257{
258 if (!(x->f & MP_NEG))
259 return mp_setbit(d, x, n);
260 d = mp_not2c(d, x);
261 d = mp_clearbit(d, d, n);
262 d = mp_not2c(d, d);
263 return (d);
264}
265
266mp *mp_clearbit2c(mp *d, mp *x, unsigned long n)
267{
268 if (!(x->f & MP_NEG))
269 return mp_clearbit(d, x, n);
270 d = mp_not2c(d, x);
271 d = mp_setbit(d, d, n);
272 d = mp_not2c(d, d);
273 return (d);
274}
275
4b536f42 276/* --- @mp_eq@ --- *
277 *
278 * Arguments: @const mp *a, *b@ = two numbers
279 *
280 * Returns: Nonzero if the numbers are equal.
281 */
282
283int mp_eq(const mp *a, const mp *b) { return (MP_EQ(a, b)); }
284
d3409d5e 285/* --- @mp_cmp@ --- *
286 *
287 * Arguments: @const mp *a, *b@ = two numbers
288 *
289 * Returns: Less than, equal to or greater than zero, according to
290 * whether @a@ is less than, equal to or greater than @b@.
291 */
292
293int mp_cmp(const mp *a, const mp *b)
294{
295 if (!((a->f ^ b->f) & MP_NEG))
296 return (mpx_ucmp(a->v, a->vl, b->v, b->vl));
297 else if (a->f & MP_NEG)
298 return (-1);
299 else
300 return (+1);
301}
302
397041a9 303/* --- @mp_neg@ --- *
304 *
305 * Arguments: @mp *d@ = destination
306 * @mp *a@ = argument
307 *
308 * Returns: The negation of the argument.
309 *
310 * Use: Negates its argument.
311 */
312
313mp *mp_neg(mp *d, mp *a)
314{
315 /* --- Surprising amounts of messing about required --- */
316
317 MP_SHRINK(a);
318 MP_COPY(a);
81578196 319 if (d)
320 MP_DROP(d);
321 if (a->v == a->vl)
397041a9 322 return (a);
397041a9 323 MP_DEST(a, MP_LEN(a), a->f);
324 a->f ^= MP_NEG;
325 return (a);
326}
327
f09e814a 328/* --- @mp_bitop@ --- *
0f32e0f8 329 *
330 * Arguments: @mp *d@ = destination
331 * @mp *a, *b@ = sources
332 *
f09e814a 333 * Returns: The result of the given bitwise operation. These functions
334 * don't handle negative numbers at all sensibly. For that, use
335 * the @...2c@ variants. The functions are named after the
336 * truth tables they generate:
337 *
338 * a: 0011
339 * b: 0101
340 * @mpx_bitXXXX@
0f32e0f8 341 */
342
f09e814a 343#define MP_BITBINOP(string) \
0f32e0f8 344 \
f09e814a 345mp *mp_bit##string(mp *d, mp *a, mp *b) \
0f32e0f8 346{ \
75263f25 347 MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), (a->f | b->f) & ~MP_NEG); \
f09e814a 348 mpx_bit##string(d->v, d->vl, a->v, a->vl, b->v, b->vl); \
0f32e0f8 349 d->f = (a->f | b->f) & MP_BURN; \
350 MP_SHRINK(d); \
351 return (d); \
352}
353
f09e814a 354MPX_DOBIN(MP_BITBINOP)
355
356/* --- @mp_not@ --- *
357 *
358 * Arguments: @mp *d@ = destination
359 * @mp *a@ = source
360 *
361 * Returns: The bitwise complement of the source.
362 */
0f32e0f8 363
364mp *mp_not(mp *d, mp *a)
365{
366 MP_DEST(d, MP_LEN(a), a->f);
367 mpx_not(d->v, d->vl, a->v, a->vl);
368 d->f = a->f & MP_BURN;
369 MP_SHRINK(d);
370 return (d);
371}
372
f09e814a 373/* --- @mp_bitop2c@ --- *
374 *
375 * Arguments: @mp *d@ = destination
376 * @mp *a, *b@ = sources
377 *
378 * Returns: The result of the given bitwise operation. Negative numbers
379 * are treated as two's complement, sign-extended infinitely to
380 * the left. The functions are named after the truth tables
381 * they generate:
382 *
383 * a: 0011
384 * b: 0101
385 * @mpx_bitXXXX@
386 */
387
388/* --- How this actually works --- *
389 *
390 * The two arguments are inverted (with a sign-swap) if they're currently
391 * negative. This means that we end up using a different function (one which
392 * reinverts as we go) for the main operation. Also, if the sign would be
393 * negative at the end, we preinvert the output and then invert again with a
394 * sign-swap.
395 *
396 * Start with: wxyz WXYZ
397 * If @a@ negative: yzwx or YZWX
398 * If @b@ negative: xwzy XWZY
399 * If both negative: zyxw ZYXW
400 */
401
402#define MP_BIT2CBINOP(n, base, an, bn, abn, p_base, p_an, p_bn, p_abn) \
403 \
404mp *mp_bit##n##2c(mp *d, mp *a, mp *b) \
405{ \
406 if (!((a->f | b->f) & MP_NEG)) { /* Both positive */ \
407 d = mp_bit##base(d, a, b); \
408 p_base \
409 } else if (!(b->f & MP_NEG)) { /* Only @b@ positive */ \
410 MP_COPY(b); \
411 d = mp_not2c(d, a); \
412 d = mp_bit##an(d, d, b); \
413 MP_DROP(b); \
414 p_an \
415 } else if (!(a->f & MP_NEG)) { /* Only @a@ positive */ \
416 MP_COPY(a); \
417 d = mp_not2c(d, b); \
418 d = mp_bit##bn(d, a, d); \
419 MP_DROP(a); \
420 p_bn \
421 } else { /* Both negative */ \
422 mp *t = mp_not2c(MP_NEW, a); \
423 mp *d = mp_not2c(d, b); \
424 d = mp_bit##abn(d, t, d); \
425 MP_DROP(t); \
426 p_abn \
427 } \
428 return (d); \
429} \
430
431#define NEG d = mp_not2c(d, d);
432#define POS
433MP_BIT2CBINOP(0000, 0000, 0000, 0000, 0000, POS, POS, POS, POS)
434MP_BIT2CBINOP(0001, 0001, 0100, 0010, 0111, POS, POS, POS, NEG)
435MP_BIT2CBINOP(0010, 0010, 0111, 0001, 0100, POS, NEG, POS, POS)
436MP_BIT2CBINOP(0011, 0011, 0011, 0011, 0011, POS, NEG, POS, NEG)
437MP_BIT2CBINOP(0100, 0100, 0001, 0111, 0010, POS, POS, NEG, POS)
438MP_BIT2CBINOP(0101, 0101, 0101, 0101, 0101, POS, POS, NEG, NEG)
439MP_BIT2CBINOP(0110, 0110, 0110, 0110, 0110, POS, NEG, NEG, POS)
440MP_BIT2CBINOP(0111, 0111, 0010, 0100, 0001, POS, NEG, NEG, NEG)
441MP_BIT2CBINOP(1000, 0111, 0010, 0100, 0001, NEG, POS, POS, POS)
442MP_BIT2CBINOP(1001, 0110, 0110, 0110, 0110, NEG, POS, POS, NEG)
443MP_BIT2CBINOP(1010, 0101, 0101, 0101, 0101, NEG, NEG, POS, POS)
444MP_BIT2CBINOP(1011, 0100, 0001, 0111, 0010, NEG, NEG, POS, NEG)
445MP_BIT2CBINOP(1100, 0011, 0011, 0011, 0011, NEG, POS, NEG, POS)
446MP_BIT2CBINOP(1101, 0010, 0111, 0001, 0100, NEG, POS, NEG, NEG)
447MP_BIT2CBINOP(1110, 0001, 0100, 0010, 0111, NEG, NEG, NEG, POS)
448MP_BIT2CBINOP(1111, 0000, 0000, 0000, 0000, NEG, NEG, NEG, NEG)
449#undef NEG
450#undef POS
451
452/* --- @mp_not2c@ --- *
453 *
454 * Arguments: @mp *d@ = destination
455 * @mp *a@ = source
456 *
457 * Returns: The sign-extended complement of the argument.
458 */
459
460mp *mp_not2c(mp *d, mp *a)
461{
462 mpw one = 1;
463
464 MP_DEST(d, MP_LEN(a) + 1, a->f);
465 if (d == a) {
466 if (a->f & MP_NEG)
467 MPX_USUBN(d->v, d->vl, 1);
468 else
469 MPX_UADDN(d->v, d->vl, 1);
470 } else {
471 if (a->f & MP_NEG)
472 mpx_usub(d->v, d->vl, a->v, a->vl, &one, &one + 1);
473 else
474 mpx_uadd(d->v, d->vl, a->v, a->vl, &one, &one + 1);
475 }
476 d->f = (a->f & (MP_NEG | MP_BURN)) ^ MP_NEG;
477 MP_SHRINK(d);
478 return (d);
479}
480
d3409d5e 481/* --- @mp_add@ --- *
482 *
483 * Arguments: @mp *d@ = destination
ef5f4810 484 * @mp *a, *b@ = sources
d3409d5e 485 *
486 * Returns: Result, @a@ added to @b@.
487 */
488
ef5f4810 489mp *mp_add(mp *d, mp *a, mp *b)
d3409d5e 490{
d34decd2 491 MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f);
d3409d5e 492 if (!((a->f ^ b->f) & MP_NEG))
493 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
494 else {
495 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
ef5f4810 496 mp *t = a; a = b; b = t;
d3409d5e 497 }
498 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
499 }
500 d->f = ((a->f | b->f) & MP_BURN) | (a->f & MP_NEG);
501 MP_SHRINK(d);
502 return (d);
503}
504
505/* --- @mp_sub@ --- *
506 *
507 * Arguments: @mp *d@ = destination
ef5f4810 508 * @mp *a, *b@ = sources
d3409d5e 509 *
510 * Returns: Result, @b@ subtracted from @a@.
511 */
512
ef5f4810 513mp *mp_sub(mp *d, mp *a, mp *b)
d3409d5e 514{
515 unsigned sgn = 0;
d34decd2 516 MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f);
d3409d5e 517 if ((a->f ^ b->f) & MP_NEG)
518 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
519 else {
520 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
ef5f4810 521 mp *t = a; a = b; b = t;
d3409d5e 522 sgn = MP_NEG;
523 }
524 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
525 }
526 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ sgn) & MP_NEG);
527 MP_SHRINK(d);
528 return (d);
529}
530
531/* --- @mp_mul@ --- *
532 *
533 * Arguments: @mp *d@ = destination
ef5f4810 534 * @mp *a, *b@ = sources
d3409d5e 535 *
536 * Returns: Result, @a@ multiplied by @b@.
537 */
538
ef5f4810 539mp *mp_mul(mp *d, mp *a, mp *b)
d3409d5e 540{
ef5f4810 541 a = MP_COPY(a);
542 b = MP_COPY(b);
543
52cdaca9 544 if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= MPK_THRESH) {
d34decd2 545 MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF);
ef5f4810 546 mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl);
8017495b 547 } else {
dd22938e 548 size_t m = MAX(MP_LEN(a), MP_LEN(b));
ef5f4810 549 mpw *s;
dd22938e 550 MP_DEST(d, 3 * m, a->f | b->f | MP_UNDEF);
551 s = mpalloc(d->a, 5 * m);
552 mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + 5 * m);
d34decd2 553 mpfree(d->a, s);
ef5f4810 554 }
555
d3409d5e 556 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
557 MP_SHRINK(d);
ef5f4810 558 MP_DROP(a);
559 MP_DROP(b);
d3409d5e 560 return (d);
561}
562
563/* --- @mp_sqr@ --- *
564 *
565 * Arguments: @mp *d@ = destination
ef5f4810 566 * @mp *a@ = source
d3409d5e 567 *
568 * Returns: Result, @a@ squared.
569 */
570
ef5f4810 571mp *mp_sqr(mp *d, mp *a)
d3409d5e 572{
ef5f4810 573 size_t m = MP_LEN(a);
574
575 a = MP_COPY(a);
52cdaca9 576 if (m > MPK_THRESH) {
ef5f4810 577 mpw *s;
dd22938e 578 MP_DEST(d, 3 * m, a->f | MP_UNDEF);
579 s = mpalloc(d->a, 5 * m);
580 mpx_ksqr(d->v, d->vl, a->v, a->vl, s, s + 5 * m);
d34decd2 581 mpfree(d->a, s);
dd22938e 582 } else {
583 MP_DEST(d, 2 * m + 2, a->f | MP_UNDEF);
ef5f4810 584 mpx_usqr(d->v, d->vl, a->v, a->vl);
dd22938e 585 }
d3409d5e 586 d->f = a->f & MP_BURN;
587 MP_SHRINK(d);
ef5f4810 588 MP_DROP(a);
d3409d5e 589 return (d);
590}
591
592/* --- @mp_div@ --- *
593 *
594 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
ef5f4810 595 * @mp *a, *b@ = sources
d3409d5e 596 *
597 * Use: Calculates the quotient and remainder when @a@ is divided by
598 * @b@. The destinations @*qq@ and @*rr@ must be distinct.
599 * Either of @qq@ or @rr@ may be null to indicate that the
600 * result is irrelevant. (Discarding both results is silly.)
601 * There is a performance advantage if @a == *rr@.
602 *
603 * The behaviour when @a@ and @b@ have the same sign is
604 * straightforward. When the signs differ, this implementation
605 * chooses @r@ to have the same sign as @b@, rather than the
606 * more normal choice that the remainder has the same sign as
607 * the dividend. This makes modular arithmetic a little more
608 * straightforward.
609 */
610
ef5f4810 611void mp_div(mp **qq, mp **rr, mp *a, mp *b)
d3409d5e 612 {
613 mp *r = rr ? *rr : MP_NEW;
614 mp *q = qq ? *qq : MP_NEW;
615 mpw *sv, *svl;
616
d3409d5e 617 /* --- Set the remainder up right --- *
618 *
619 * Just in case the divisor is larger, be able to cope with this. It's not
620 * important in @mpx_udiv@, but it is here because of the sign correction.
621 */
622
d34decd2 623 b = MP_COPY(b);
624 a = MP_COPY(a);
625 if (r)
626 MP_DROP(r);
627 r = a;
a9c8f3d6 628 MP_DEST(r, MAX(MP_LEN(a), MP_LEN(b)) + 2, a->f | b->f);
d3409d5e 629
630 /* --- Fix up the quotient too --- */
631
d34decd2 632 r = MP_COPY(r);
633 MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF);
634 MP_DROP(r);
635
636 /* --- Set up some temporary workspace --- */
637
638 {
639 size_t rq = MP_LEN(b) + 1;
640 sv = mpalloc(r->a, rq);
641 svl = sv + rq;
642 }
d3409d5e 643
644 /* --- Perform the calculation --- */
645
646 mpx_udiv(q->v, q->vl, r->v, r->vl, b->v, b->vl, sv, svl);
647
648 /* --- Sort out the sign of the results --- *
649 *
650 * If the signs of the arguments differ, and the remainder is nonzero, I
651 * must add one to the absolute value of the quotient and subtract the
652 * remainder from @b@.
653 */
654
d34decd2 655 q->f = ((r->f | b->f) & MP_BURN) | ((r->f ^ b->f) & MP_NEG);
d3409d5e 656 if (q->f & MP_NEG) {
ef5f4810 657 mpw *v;
658 for (v = r->v; v < r->vl; v++) {
d3409d5e 659 if (*v) {
660 MPX_UADDN(q->v, q->vl, 1);
661 mpx_usub(r->v, r->vl, b->v, b->vl, r->v, r->vl);
662 break;
663 }
664 }
665 }
666
d34decd2 667 r->f = ((r->f | b->f) & MP_BURN) | (b->f & MP_NEG);
d3409d5e 668
669 /* --- Store the return values --- */
670
d34decd2 671 mpfree(r->a, sv);
672 MP_DROP(b);
673
d3409d5e 674 if (!qq)
675 MP_DROP(q);
676 else {
677 MP_SHRINK(q);
678 *qq = q;
679 }
680
681 if (!rr)
682 MP_DROP(r);
683 else {
684 MP_SHRINK(r);
685 *rr = r;
686 }
d3409d5e 687}
688
f1713c63 689/* --- @mp_odd@ --- *
690 *
691 * Arguments: @mp *d@ = pointer to destination integer
692 * @mp *m@ = pointer to source integer
693 * @size_t *s@ = where to store the power of 2
694 *
695 * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%.
696 *
697 * Use: Computes a power of two and an odd integer which, when
698 * multiplied, give a specified result. This sort of thing is
699 * useful in number theory quite often.
700 */
701
702mp *mp_odd(mp *d, mp *m, size_t *s)
703{
704 size_t ss = 0;
705 const mpw *v, *vl;
706
707 v = m->v;
708 vl = m->vl;
709 for (; !*v && v < vl; v++)
710 ss += MPW_BITS;
711 if (v >= vl)
712 ss = 0;
713 else {
714 mpw x = *v;
715 mpw mask = MPW_MAX;
716 unsigned z = MPW_BITS / 2;
717
718 while (z) {
719 mask >>= z;
720 if (!(x & mask)) {
721 x >>= z;
722 ss += z;
723 }
724 z >>= 1;
725 }
726 }
727
728 *s = ss;
729 return (mp_lsr(d, m, ss));
730}
731
d3409d5e 732/*----- Test rig ----------------------------------------------------------*/
733
734#ifdef TEST_RIG
735
736static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b)
737{
4b536f42 738 if (!MP_EQ(expect, result)) {
d3409d5e 739 fprintf(stderr, "\n*** %s failed", op);
740 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
741 fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 10);
742 fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 10);
743 fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 10);
744 fputc('\n', stderr);
745 return (0);
746 }
747 return (1);
748}
749
750#define RIG(name, op) \
ef5f4810 751 static int t##name(dstr *v) \
d3409d5e 752 { \
753 mp *a = *(mp **)v[0].buf; \
754 mpw n = *(int *)v[1].buf; \
755 mp b; \
756 mp *r = *(mp **)v[2].buf; \
757 mp *c = op(MP_NEW, a, n); \
758 int ok; \
759 mp_build(&b, &n, &n + 1); \
760 ok = verify(#name, r, c, a, &b); \
761 mp_drop(a); mp_drop(c); mp_drop(r); \
ef5f4810 762 assert(mparena_count(MPARENA_GLOBAL) == 0); \
d3409d5e 763 return (ok); \
764 }
765
766RIG(lsl, mp_lsl)
767RIG(lsr, mp_lsr)
f09e814a 768RIG(lsl2c, mp_lsl2c)
769RIG(lsr2c, mp_lsr2c)
d3409d5e 770
771#undef RIG
772
773#define RIG(name, op) \
ef5f4810 774 static int t##name(dstr *v) \
d3409d5e 775 { \
776 mp *a = *(mp **)v[0].buf; \
777 mp *b = *(mp **)v[1].buf; \
778 mp *r = *(mp **)v[2].buf; \
779 mp *c = op(MP_NEW, a, b); \
780 int ok = verify(#name, r, c, a, b); \
781 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \
ef5f4810 782 assert(mparena_count(MPARENA_GLOBAL) == 0); \
d3409d5e 783 return (ok); \
784 }
785
786RIG(add, mp_add)
787RIG(sub, mp_sub)
788RIG(mul, mp_mul)
789
790#undef RIG
791
792static int tdiv(dstr *v)
793{
794 mp *a = *(mp **)v[0].buf;
795 mp *b = *(mp **)v[1].buf;
796 mp *q = *(mp **)v[2].buf;
797 mp *r = *(mp **)v[3].buf;
798 mp *c = MP_NEW, *d = MP_NEW;
799 int ok = 1;
800 mp_div(&c, &d, a, b);
801 ok &= verify("div(quotient)", q, c, a, b);
802 ok &= verify("div(remainder)", r, d, a, b);
803 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q);
ef5f4810 804 assert(mparena_count(MPARENA_GLOBAL) == 0);
d3409d5e 805 return (ok);
806}
807
f09e814a 808static int tbin(dstr *v)
809{
810 static mp *(*fn[])(mp *, mp *, mp *) = {
811#define DO(string) mp_bit##string##2c,
812MPX_DOBIN(DO)
813#undef DO
814 };
815 int ok = 1;
816 unsigned op = 0;
817 mp *a = *(mp **)v[1].buf;
818 mp *b = *(mp **)v[2].buf;
819 mp *r = *(mp **)v[3].buf;
820 mp *c;
821
822 if (strcmp(v[0].buf, "and") == 0) op = 1;
823 else if (strcmp(v[0].buf, "or") == 0) op = 7;
824 else if (strcmp(v[0].buf, "nand") == 0) op = 14;
825 else if (strcmp(v[0].buf, "nor") == 0) op = 8;
826 else if (strcmp(v[0].buf, "xor") == 0) op = 6;
827 else {
828 char *p = v[0].buf;
829 while (*p) {
830 op <<= 1;
831 if (*p++ == '1')
832 op |= 1;
833 }
834 }
835
836 c = fn[op](MP_NEW, a, b);
837 ok = verify(v[0].buf, r, c, a, b);
838 mp_drop(a); mp_drop(b); mp_drop(r); mp_drop(c);
839 assert(mparena_count(MPARENA_GLOBAL) == 0);
840 return (ok);
841}
842
09d00c6b 843static int tset(dstr *v)
844{
845 mp *a = *(mp **)v[0].buf;
846 unsigned long n = *(unsigned long *)v[1].buf;
847 mp *r = *(mp **)v[2].buf;
848 mp *c;
849 int ok = 1;
850
851 c = mp_setbit2c(MP_NEW, a, n);
852 if (!MP_EQ(c, r)) {
853 ok = 0;
854 fprintf(stderr, "\n***setbit (set) failed");
855 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16);
856 fprintf(stderr, "\n*** n = %lu", n);
857 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
858 fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16);
859 fputc('\n', stderr);
860 }
861 if (!mp_testbit2c(r, n)) {
862 ok = 0;
863 fprintf(stderr, "\n***setbit (test) failed");
864 fprintf(stderr, "\n*** n = %lu", n);
865 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
866 fputc('\n', stderr);
867 }
868 mp_drop(a);
869 mp_drop(r);
870 mp_drop(c);
871 assert(mparena_count(MPARENA_GLOBAL) == 0);
872 return (ok);
873}
874
875static int tclr(dstr *v)
876{
877 mp *a = *(mp **)v[0].buf;
878 unsigned long n = *(unsigned long *)v[1].buf;
879 mp *r = *(mp **)v[2].buf;
880 mp *c;
881 int ok = 1;
882
883 c = mp_clearbit2c(MP_NEW, a, n);
884 if (!MP_EQ(c, r)) {
885 ok = 0;
886 fprintf(stderr, "\n***clrbit (set) failed");
887 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16);
888 fprintf(stderr, "\n*** n = %lu", n);
889 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
890 fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16);
891 fputc('\n', stderr);
892 }
893 if (mp_testbit2c(r, n)) {
894 ok = 0;
895 fprintf(stderr, "\n***clrbit (test) failed");
896 fprintf(stderr, "\n*** n = %lu", n);
897 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
898 fputc('\n', stderr);
899 }
900 mp_drop(a);
901 mp_drop(c);
902 mp_drop(r);
903 assert(mparena_count(MPARENA_GLOBAL) == 0);
904 return (ok);
905}
906
397041a9 907static int tneg(dstr *v)
908{
909 mp *a = *(mp **)v[0].buf;
910 mp *r = *(mp **)v[1].buf;
911 int ok = 1;
912 mp *n = mp_neg(MP_NEW, a);
913 if (!MP_EQ(r, n)) {
914 ok = 0;
915 fprintf(stderr, "\n*** neg failed\n");
916 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
917 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10);
918 fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10);
919 fputc('\n', stderr);
920 }
921 mp_drop(n);
922 n = mp_neg(a, a);
923 if (!MP_EQ(r, n)) {
924 ok = 0;
925 fprintf(stderr, "\n*** neg failed\n");
926 fputs("\n*** a* = ", stderr); mp_writefile(a, stderr, 10);
927 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10);
928 fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10);
929 fputc('\n', stderr);
930 }
931 mp_drop(a);
932 mp_drop(r);
933 assert(mparena_count(MPARENA_GLOBAL) == 0);
934 return (ok);
935}
936
f1713c63 937static int todd(dstr *v)
938{
939 mp *a = *(mp **)v[0].buf;
940 size_t rs = *(uint32 *)v[1].buf;
941 mp *rt = *(mp **)v[2].buf;
942 int ok = 1;
943 mp *t;
944 size_t s;
945 t = mp_odd(MP_NEW, a, &s);
4b536f42 946 if (s != rs || !MP_EQ(t, rt)) {
f1713c63 947 ok = 0;
948 fprintf(stderr, "\n*** odd failed");
949 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
950 fprintf(stderr, "\n*** s = %lu", (unsigned long)s);
951 fputs("\n*** t = ", stderr); mp_writefile(t, stderr, 10);
952 fprintf(stderr, "\n*** rs = %lu", (unsigned long)rs);
953 fputs("\n*** rt = ", stderr); mp_writefile(rt, stderr, 10);
954 fputc('\n', stderr);
955 }
956 mp_drop(a);
957 mp_drop(rt);
958 mp_drop(t);
09d00c6b 959 assert(mparena_count(MPARENA_GLOBAL) == 0);
f1713c63 960 return (ok);
961}
962
d3409d5e 963static test_chunk tests[] = {
f09e814a 964 { "lsl", tlsl, { &type_mp, &type_int, &type_mp, 0 } },
965 { "lsr", tlsr, { &type_mp, &type_int, &type_mp, 0 } },
966 { "lsl2c", tlsl2c, { &type_mp, &type_int, &type_mp, 0 } },
967 { "lsr2c", tlsr2c, { &type_mp, &type_int, &type_mp, 0 } },
09d00c6b 968 { "setbit", tset, { &type_mp, &type_ulong, &type_mp, 0 } },
969 { "clrbit", tclr, { &type_mp, &type_ulong, &type_mp, 0 } },
d3409d5e 970 { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } },
971 { "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } },
972 { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } },
973 { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
f09e814a 974 { "bin2c", tbin, { &type_string, &type_mp, &type_mp, &type_mp, 0 } },
f1713c63 975 { "odd", todd, { &type_mp, &type_uint32, &type_mp, 0 } },
397041a9 976 { "neg", tneg, { &type_mp, &type_mp, 0 } },
d3409d5e 977 { 0, 0, { 0 } },
978};
979
980int main(int argc, char *argv[])
981{
982 sub_init();
983 test_run(argc, argv, tests, SRCDIR "/tests/mp");
984 return (0);
985}
986
987#endif
988
989/*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)